If I think about cutting the logs, it is true that they need to be cut one way or the other (before you sew, or after you sew). However, I find that the *sewing* goes much faster using strips. Others may well be more adept, but I find that I lose a lot of time picking up two log pieces and matching them exactly before sewing. I enjoy picking up just one piece and adding it to the strip already lined up on my sewing machine.
Also, for me it is much more enjoyable to cut apart finished sewn pieces than to cut raw fabric. The one time I tried the Judy Martin way, I made several cutting mistakes on the logs and had to re-cut some stacks down. When cutting after the pieces are already sewn to a strip, I don't make that kind of mistake.
As I said, though, I have not made a really complex log cabin quilt; I've always stuck to the plain vanilla versions. I do think pre-cutting has more value when making a Judy Martin type of log cabin quilt that has a *lot* of narrow pieces of different sizes. I simply have not found it necessary for the type of log cabin quilt I make; the degree of accuracy I get is fine for them. Plus, I get more pleasure out of the Eleanor Burns method. Other quilters may get more pleasure out of the Judy Martin method. It probably depends a lot on personality and what an individual quilter is looking to get out of the process.
The only thing I would deeply caution against is cutting log cabin pieces on the bias!!!